Zach J.

How would I evaluate limx→0 (x + cos(x))^(1/x) using l'hopital's rule? I am using the rule of logs to simplify the expression to (1/x)*ln(x+cos(x)), but I am unsure of how to go on from there.

In Deutsch's algorithm, we are provided some black-box Uf which acts as a switch on the target qubit, governed by the value of f evaluated at the control qubit state. That is, Uf acts as an... more

Use Stokes' Theorem to evaluate ∫∫S curl F · dS.F(x,y,z) = exycos(z) i + x2z j + xy k S is the hemisphere , oriented in the direction of the positive x-axis.

Find the derivative of the following function𝐹(𝑥)= ∫𝑥^3 (upper) 𝑥^2(lower) (2𝑡−1)^3𝑑𝑡using the Fundamental Theorem of Calculus. 𝐹′(𝑥) = ?

Find the area above the curve of 3x2 – 12x + 9 from [1, 3]. What I know is that the solution would involve infinite summation. The place where I am stuck is the definition of the sum. I know... more

Question #1. a) For all mxn matrices A such that A^tA is invertible, show that P=A(A^tA)^-1A^t is an orthogonal projection. b) Explain why, if u is an nx1 unit column vector in Rn, part a) shows... more